tunguska - (c) Diane Neisius (diane_va@yahoo.com) - GPL'ed free software - Contents 0. Introduction 1. Installation 2. Description of the Program 3. Examples 4. Problems 5. References 0. Introduction Tunguska was programmed by me following the paper of Hill and Goda [1]. The goal was twofold: amateur astronomer's interest in events like Tunguska 1908 and the search for a nice exercise in learning the C programming language. IMPORTANT: The program is for amateur scientific research in the interaction of meteoroides and atmosphere, not for entertainment purposes! Such surely will not be satisfied by the output of long columns of numbers! C hackers surely will giggle about my programming style - I developed scientific software using FORTRAN and PASCAL for some years of my life in research. Doing it, I found it more important to have readable source code than to tune for some nanoseconds. Today, optimizing compilers and gigahertz processors make this goal more obsolete than twenty years ago. Solingen/Germany, January 16, 2002 - Diane Neisius, Ph. D. 1. Installation Installation of tunguska is quite simple by the make command. At least if a C compiler and make are installed on your system. After unpacking the downloaded file by gunzip and tar to some directory of your choice, change via cd to /tunguska and type "make" - then all else should happen automatically. The program was developed on a Linux system using the GNU C compiler "gcc 2.95". For the fact I used no special tricks it should compile and run on other systems as well. 2. Description of the Program Tunguska uses differential equations of motion and of ablationfrom a paper by Hill and Goda [1]. These equations describe in a simple way the movement and mass loss of an asteroid or meteoroid in the earth's atmosphere. The solution of the equations is performed numerically by a Runge-Kutta scheme of 4th order. The program expects the input data from a file named tunguska.in, which must be located in the actual directory. It reads a char specifying the material of the meteoroid (iron, silicate or chondrite), the diameter, the speed and the angle it toches the atmosphere. The last value is the time step which will be used to compute the solution values. Output for a time step is: exact time in seconds, mass of meteoroid in tons, actual speed in km/s, actual heigth in km, actual traveled path over ground in km, diameter of the meteoroid in meters and the absolute magniude (normed to a distance of 100 km). Diameter here means the body itself only if it didn`t break up yet, otherwise it is the diameter of the debris cloud! The particular events like break up, separation etc. will be noted between the solution lines by a short message if they occur. Normally, the program runs through a couple of phases. First the meteoroid entering the atmosphere only is decelerated and ablates. Somewhen the ram pressure surpasses the material strength, the body breaks up in a debris cloud ("inital breakup"). Soon the debris has moved apart enough to feel the ram pressure for itself in full. The higher stages of fragmentation begin ("fragmentation continues"). If the debris cloud is decelerated by aerobraking still more, the ram pressure lowers and the fragmentation stops ("fragmentation stops"). The debris still moves more apart, the diameter of the cloud increases more and more, until the cloud can't viewed any longer as a coherent object ("separation,..."). Then, the biggest fragment out of the cloud is traced until the program stops. It does if there is an impact to the earth's surface or the rest mass of the meteoroid is ablated ("burned") totally. Of course there aren't all this phases in all computed cases. Iron meteoroids, for example, tend to break all the way down until impact. Some smaller meteoroids have only initial breakup, after which the fragmentation immediately stops. Some modifications have been done against the original method. First, the gravitational acceleration is viewed as a constant, for the traced paths are short with respect to earth's radius. Second, the trajectory over ground is added as a variable, and the curvature of the earth's atmosphere is introduced. This makes it possible to compute also "atmosphere grazers" like the Montana fireball of 1972 [2,3] - which was not possible using the original method of Hill and Goda. Of course this implies there must be another program stop - at the point the meteoroid leaves the atmosphere. It was a conscious decision not to use the formula of blastwave damage from Hill's and Goda's paper. I didn't like to use result from nuclear weapons research. 3. Examples Some well-known examples of big bolides has been documented in tunguska/examples (every case with input and output). Tunguska 1908 [4]: Name-giving to the program, today is supposed the Tunguska explosion was caused by a chondritic meteoroid of 80 meters. The simulation shows how the body breaks up in fragments in kilogram size. Moreover, the results also shows the fragments are decelerated soon to a speed range in which the earth's rotation of 1600 m/s is no longer negligible - which explains the observed change in direction during the flight. Sikhote Alin 1947 [5]: Of this iron meteoroid a lot of pieces have been recovered (I owe two small of it). Originally there was a relatively small speed of 14.5 km/s supposed, but the computation shows this doesn't break an iron body of this size. Higher velocities of 18 and 22 km/s give us an appropriate debris ellipse or a biggest fragment of ton-size (as recovered), but not both similar in one run. Here we see the limits of the used model, which obviously cannot describe exactly the inhomogeneous "lumpy" body, whose pieces had a so different behaviour. Barringer crater: For this crater in Arizona probably signs an iron meteoroid of 60 meters. The result shows it must have been as slow as 12 km/s, otherwise it would have been fragmented. Montana fireball 1972 [2,3]: Bartky, Gordon and Li suppose this iron meteoroid to be of 50 meters. This doesn't fit to the observed brightness of -19 mag, as the computation shows. It will be met by a body of only 15 meters better. The fireball leaves the atmosphere after a travel of nearly 2000 km over ground and a flight time of 2 minutes without breaking up. Of course the last example digs up the question, how close a meteoroid can come to earth without impact - or, in reverse, when doesn't it escape any more? Who likes to see a 20-min odysee between sky and earth should input the data of the Montana fireball to Tunguska and change the angle to 7.788 degrees... 4. Problems To prevent problems at input, the file tunguska.in should be changed only in overwrite mode. Problems at output occur if the time step of the Runge Kutta method isn't correct. In doubt, reduce it! During the run, the size of the time step is reduced automatically in critical phases. Nevertheless there should be more than one time step during a single phase of the program run. An idea of convenient values for the timestep you can get from tunguska/examples. General rule is, smaller meteoroids need smaller time steps for the deceleration is higher. The "endless falling" of small fragments after separation can't be prevented in every case. The time step automatically is increased drastically, if becoming slower than sound speed. Not always enough to shorten a long output list, but the behayiour of the equations can't be predicted in a simple way to do it. If you've got problems in compiling for your C compiler doesn't know the constant M_PI, simply enter the value 3.14... by hand in the main program (tunguska.c line 32). 5. References [1] Hill / Goda The Fragmentation of Small Asteroids in the Atmosphere Astr. J. 105(1993) p. 1114 [2] A Great Daylight Fireball over the Northwest Sky & Telescope, Oct. 1972 p. 269 [3] Bartky/ Gordon / Li (Letter) Sky & Telescope April 1973 p. 219 [4] R. Gallant Journey to Tunguska Sky & Telescope June 1994 p. 38 [5] R. Gallant Sikhote Alin - Fifty Years Later Sky & Telescope Feb. 1997 p. 50